One body, two sides. Picture a line painted on the ground and a person standing over it with one foot on each side. They are not on this side, and not on that side; they are on both at the same time. Every use of straddle can be read as that same picture getting larger. The line becomes a river, then a national border, then the edge between two subjects, then the two halves of an argument. Whatever is in the middle stays in the middle, and whatever straddles it keeps touching both sides at once.
From the word’s history
The source says the verb is recorded from the 1560s and is most likely an altered form of the dialect word striddle. That is as far as this evidence goes; no older root is given, so treat it as a note about the word's age rather than an explanation of the picture.
資料說這個動詞從 1560 年代就有紀錄，來源「很可能」是方言字 striddle。線索到這裡就停了，沒有更早的字根，所以把它當成一個年代的註記就好，不要當成上面那個畫面的來源解釋。
Wiktionary, "straddle"
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